Use the sleep command.

Example:

sleep .5 # Waits 0.5 second.
sleep 5  # Waits 5 seconds.
sleep 5s # Waits 5 seconds.
sleep 5m # Waits 5 minutes.
sleep 5h # Waits 5 hours.
sleep 5d # Waits 5 days.

One can also employ decimals when specifying a time unit; e.g. sleep 1.5s

Bash has a "loadable" sleep which supports fractional seconds, and eliminates overheads of an external command:

$ cd bash-3.2.48/examples/loadables
$ make sleep && mv sleep sleep.so
$ enable -f sleep.so sleep

Then:

$ which sleep
/usr/bin/sleep
$ builtin sleep
sleep: usage: sleep seconds[.fraction]
$ time (for f in `seq 1 10`; do builtin sleep 0.1; done)
real    0m1.000s
user    0m0.004s
sys     0m0.004s

The downside is that the loadables may not be provided with your bash binary, so you would need to compile them yourself as shown (though on Solaris it would not necessarily be as simple as above).

As of bash-4.4 (September 2016) all the loadables are now built and installed by default on platforms that support it, though they are built as separate shared-object files, and without a .so suffix. Unless your distro/OS has done something creative (sadly RHEL/CentOS 8 build bash-4.4 with loadable extensions deliberately removed), you should be able to do instead:

[ -z "$BASH_LOADABLES_PATH" ] &&
  BASH_LOADABLES_PATH=$(pkg-config bash --variable=loadablesdir 2>/dev/null)  
enable -f sleep sleep

(The man page implies BASH_LOADABLES_PATH is set automatically, I find this is not the case in the official distribution as of 4.4.12. If and when it is set correctly you need only enable -f filename commandname as required.)

If that's not suitable, the next easiest thing to do is build or obtain sleep from GNU coreutils, this supports the required feature. The POSIX sleep command is minimal, older Solaris versions implemented only that. Solaris 11 sleep does support fractional seconds.

As a last resort you could use perl (or any other scripting that you have to hand) with the caveat that initialising the interpreter may be comparable to the intended sleep time:

$ perl -e "select(undef,undef,undef,0.1);"
$ echo "after 100" | tclsh

When a Bash script is running a sleep, here's what the pstree might look like:

bash(10102)───sleep(8506)

Both have process IDs (PIDs), even when running as a script. If we wanted to interrupt the sleep, we'd send kill 8506 and the Bash session would resume... The problem is in a scripted environment we don't know the PID of the sleep command and there isn't a human to look at the process tree.

We can get the PID of the Bash session through the $$ magic variable. If we can store that somewhere, we can then target instances of sleep that are running underneath that PID. Here's what I'd put in the script:

# write the current session's PID to file
echo $$ >> myscript.pid

# go to sleep for a long time
sleep 1000

And then we can tell pkill to nuke sleep instances running underneath that PID:

pkill -P $(<myscript.pid) sleep

Again, this is limiting itself to only sleep processes running directly under that one Bash session. As long as the PID was logged correctly, this makes it a lot safer than killall sleep or pkill sleep, which could nuke any sleep process on the system (permissions allowing).

We can prove that theory with the following example where we have three separate bash sessions, two running sleep. Only because we're specifying the PID of the top-left bash session, only its sleep is killed.

An alternative approach is to push sleep into the background, store its PID and then return it to the foreground. In the script:

sleep 1000 &
echo $! > myscript.sleep.pid
fg

And to kill it:

kill $(<myscript.sleep.pid)